Closed-form Symbol Error Rate Research Articles

Theoretical Performance of LoRa System in Multipath and Interference Channels

This paper presents a semi-analytical approximation of Symbol Error Rate (SER) for the well known LoRa Internet of Things (IoT) modulation scheme in the following two scenarios: 1) in multi-path frequency selective fading channel with Additive White Gaussian Noise (AW GN) and 2) in the presence of a second interfering LoRa user in flat-fading AW GN channel. Performances for both coherent and non-coherent cases are derived by considering the common Discrete Fourier transform (DF T) based detector on the received LoRa waveform. By considering these two scenarios, the detector exhibits parasitic peaks that severely degrade the performance of the LoRa receiver. We propose in that sense a theoretical expression for this result, from which a unified framework based on peak detection probabilities allows us to derive SER, which is validated by Monte Carlo simulations. Fast computation of the derived closedform SER allows to carry out deep performance analysis for these two scenarios.

Error performance analysis of optical communication over Lognormal-Rician turbulence channel using Gram-Charlier Series

Abstract In this paper, the symbol-error rate (SER) performance of a coherent free-space optical (FSO) communication system in lognormal-Rician turbulence channel is analyzed using the generalized Gram-Charlier (GCC) series. We proposed the differential evolution (DE) algorithm to solve the parameters in GCC efficiently. It is shown that highly accurate closed-form SER expressions are obtained for M-ary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) schemes with maximum ratio combining (MRC) technique. The asymptotic error rate analysis is presented to reveal the performance behavior in the high signal-to-noise (SNR) regime. The effects of imperfect phase noise compensation on the error rate performance are also studied, and it is found that the impact of phase compensation error can be small enough with loop SNR ρ c more than seven.

SER performance investigation of a MPPM relay-aided FSO system with three decision thresholds over EW fading channel considering pointing errors

The symbol error rate (SER) performance of a multi-hop parallel free-space optical (FSO) communication system with multiple pulse position modulation (MPPM) scheme considering three different decision threshold schemes, fixed decision threshold (FDT), optimized decision threshold (ODT), and dynamic decision threshold (DDT) has been investigated over exponentiated Weibull (EW) atmospheric turbulence channel combiningthe impact of the fading induced by pointing errors. On the basis of the decode-and-forward (DF) protocol, the cumulative distribution function (CDF) and probability density function (PDF) in terms of the Meijer’ s G-function for this considered FSO communication system are derived with the max–min criterion as the best path selection scheme. After that, the closed-form SER expressions for three threshold schemes are obtained by Gauss–Laguerre quadrature function and then confirmed by Monte Carlo (MC) simulation. The SER performance is further analyzed systematically under different turbulence conditions, receiver aperture sizes, jitter variances, and structure parameters (R and C) for three decision threshold schemes. The results show that pointing errors will deteriorate the system performance, while the multi-hop parallel transmission can improve the SER performance and expand the communication range. Furthermore, ODT and DDT schemes can significantly overcome the effect of the error floor of FDT scheme. This work benefits the development of the MPPM based relay-aided FSO system.

Analysis and Design of Rateless Two-way Relay Networks Based on a Multiply-and-Forward Scheme

In this paper, we propose a rateless, three-stage, two-way multiply-and-forward (MF) relaying system over the Rayleigh flat fading channel, where two source nodes communicate with each other through a relay node and all nodes work on half-duplex and time-division mode. We thoroughly analyze the signals during all three stages in the proposed MF system and derive the closed-form symbol error rate (SER) expressions for an uncoded MF-two-way relay network (MF-TWRN). Furthermore, we provide the equivalent point-to-point fading channel model, which is employed to carry out the asymptotic performance analysis. We finally put forth an optimization model for the MF-TWRN with fountain codes. Simulation results show that our optimized degree distribution can provide outstanding performance for the MF-TWRN compared to those in the literature.

Phase-Jitter based SER of MPSK Scheme over Generalised Mixture Gamma Fading

ABSTRACTExtensive literature exists for simple and exact expressions of symbol error rate (SER) over fading channels under different modulation schemes whose boundaries meet at right angles. In cases where boundaries do not meet at right angles, integrals of special function in the expressions make the exact calculation most complex. In such cases only approximate solutions are possible. Also, it is noteworthy to mention that when detection is performed with proper use of the phase (phase-jitter-based approach), noise performance of the receiver improves significantly. This paper applies phase-jitter PDF-based approach to present exact and closed-form SER expression of MPSK scheme over Mixture Gamma (MG) distribution for an arbitrary array of signal points. The proposed expression is generic as MG distribution can be approximated in almost all fading/shadowed fading channel models. As a proof to the authenticity, SERs of MPSK scheme over Rayleigh and Nakagami-m fading channels are deduced from the proposed SER over generalised MG distribution. Further, a significant improvement in SER has been achieved with phase-jitter-based approach as compared to conventional (non-phase-jitter-based) approach. Finally, to confirm the correctness of the proposed expression, results are validated through comparison with the existing results and Monte Carlo simulation.

Probability of Error in MMSE Detection For MIMO-FBMC-OQAM Systems

This work calculates closed-form symbol error rate (SER) expression for minimum mean square error (MMSE) detection in low-frequency selective multiple-input multiple-output (MIMO) filter bank multicarrier (FBMC) systems with offset quadrature amplitude modulation (OQAM). To achieve this aim, we first derive, by assuming perfect receive channel state information, the probability distribution function (PDF) of the post-processing signal-to-noise-plus-interference-ratio for MMSE combining in small MIMO-FBMC-OQAM systems. The PDF is then used to derive the closed-form SER expression. We show that the performance of the derived SER expression matches with its numerical counterpart.

Closed-Form Symbol Error Rate Expressions for Non-Orthogonal Multiple Access Systems

In this paper, the reliability performance of a non-orthogonal multiple access (NOMA) system is addressed. We characterize the reliability performance of the users in a downlink power domain NOMA system with arbitrary ordered pulse-amplitude modulation and quadrature amplitude modulation. In particular, the exact symbol error rate (SER) expressions are derived. Furthermore, by taking the power allocation between users into account, a reliability optimization problem is formulated, which minimizes the SER of the user with a good channel quality while guaranteeing the reliability requirement for the user with a relatively poor channel. Based on the characterized SER model, a suboptimal power allocation approach for this problem is provided with a performance extremely close to the optimal solution. Through simulations, we validate the provided SER characterization and confirm the effectiveness of the proposed suboptimal power allocation policy.

IoT Communications With <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math> </inline-formula>-PSK Modulated Ambient Backscatter: Algorithm, Analysis, and Implementation

Ambient backscatter (AB), making use of both energy harvesting and backscattering, has recently become a promising solution to communications among low-power devices and demonstrates its potential application in the Internet of Things. Existing AB systems adopt two-state amplitude shift keying or phase shift keying (PSK), where data are transmitted at the rate of one bit per symbol period. To increase the data rate, we investigate the high-order modulation where ${M}$ -PSK is employed for backscattering. We derive the optimal multilevel energy detector and compute the closed-form symbol error rate. To show the realizability of the proposed design, we build a 4PSK-AB hardware prototype, in which the selection of load impedance is discussed with the aid of phasor diagram illustration. The hardware prototype can achieve the date rate of 20 kb/s. Besides, higher date rate is achievable for 98.7% of the time compared with binary AB communications, and the mean number of distinguishable symbols is 3.66.

Exact error rate analysis of two-hop AF Rayleigh fading cooperative systems with variable amplification gain

A careful exploration of literature confirms that exact symbol-error-rate (SER) performance of amplify-and-forward (AF) wireless cooperative communication systems with variable amplification gain has not been analyzed before; even for simple models with single relay (i.e, two-hop systems) and Rayleigh fading channels. The main source of this mathematical intractability is the appearance of the modified Bessel function of the second type Kν(·) in the statistics of these systems end-to-end SNR. Here, however, we aim at filling this literature gap by proposing a novel theoretical method that helps in examining, for the first time, the exact SER performance of two-hop AF systems, where, as a case study, we assume Rayleigh quasi-static fading environment with perfect channel estimation. Specifically, we derive two new exact expressions for the system’s SER performance, which involve rapidly convergent infinite summation(s) and efficiently computable special functions. Furthermore, for the same system, we obtain new approximate closed-form SER expression, which outperforms its literature counterpart. The obtained analytical results are useful to gain insight about the actual error performance of variable gain AF systems. The presented methodologies can form a generic framework for exact SER performance evaluation of other variable gain AF cooperative system models.

Impact of pointing errors on the SER performance of free space optical communication system with two decision thresholds over exponentiated Weibull fading channels

The impact of pointing errors on the symbol error rate (SER) performance of multiple pulse-position modulation (MPPM) free space optical (FSO) system with optimized decision threshold (ODT) and dynamic decision threshold (DDT) is investigated over exponentiated Weibull atmospheric turbulence channels. The probability density function (PDF) of the aggregated channel model is derived on the basis of Meijer’s G-function and the closed-form SER expression is then obtained by Gauss–Laguerre quadrature function. The variations of SER performance with different jitter variances, beam width, aperture sizes, and turbulence strengths for these two decision threshold schemes are analyzed in detail. The study shows that the impact of jitter variances is more apparent for ODT than that for DDT scheme and the performance difference between ODT and DDT schemes decreases with the increase of beam width. Monte Carlo simulation is also provided to verify the correctness of the proposed SER models. This work is beneficial to the design of FSO system.

Performance analysis of scheduled STBC using statistical CSI under multiple interferers with different power in CR-MIMO systems

This paper studies the impact of the multiple interferers with different power on performance of a scheduled space–time block coding (STBC) using the statistical channel state information (CSI) in cognitive radio-multiple input multiple output (CR-MIMO) systems. This paper derives the exact closed-form cumulative density function (CDF) expression of the instantaneous post-processing signal to noise plus interference ratio (SINR) random variable at the user terminal of the proposed system. Using the derived CDF, the exact closed-form symbol error rate (SER) expression of the proposed system is derived for M-ary quadrature amplitude modulations (QAM). Further, this paper derives the exact closed-form expressions of outage probability and capacity for the proposed system. From the results, we know that the performance of the proposed system is saturated at different peak power constraint depending on the peak interference constraint. Also, the performance floor gets better by multi-user diversity and receive spatial diversity below the peak interference constraint in the presence of multiple interferers.

Rician-Nakagami 페이딩 채널에서 M-PSK와 M-DPSK 시스템에 대한 효과적인 점근적 심볼 에러 확률 성능 분석

Using the existing exact but quite complicated symbol error rate (SER) expressions for M-ary phase shift keying (M-PSK) and M-ary differential phase shift keying (M-DPSK), we derive effective and concise closed-form asymptotic SER formulas especially in Rician-Nakagami fading channels. The derived formulas can be utilized to efficiently verify the achievable error rate performances of M-PSK and M-DPSK systems for the Rician-Nakagami fading environments. In addition, by exploiting the modulation gains directly obtained from the asymptotic SER formulas, we also theoretically demonstrate that M-DPSK suffers an asymptotic SER performance loss of 3.01dB with respect to M-PSK for a given M in Rician-Nakagami fading channels at high signal-to-noise ratio (SNR).

Concise SER Analysis of Differential Quaternary Phase Shift Keying with Gray Coding Over Composite Multipath Shadowing Channels

To effectively assess the symbol error rate (SER) performance achieved by π/4 differential quaternary phase shift keying (π/4-DQPSK) with Gray coding over Rician-Nakagami fading channels, a simple closed-form asymptotic SER formula is derived, which is much simpler than the existing exact SER expression. From the proposed simple closed-form formula, we can obtain some useful insights into the achievable error rate performance for the DQPSK modulation with Gray coding for various channel conditions in the high signal-to-noise ratio (SNR) regions.

Fixed-gain AF PLNC over cascaded Nakagami-m fading channels for vehicular communications

We propose an inter-vehicle communication system and investigate its performance. Due to employing physical layer network coding (PLNC) with fixed gain amplify-and-forward (AF) scheme on relay, our system is more practical in terms of implementation complexity than the ones using variable gain. Analytic results are derived under the cascaded Nakagami-m fading channel model assumption covering cascaded Rayleigh, double Nakagami-m, Generalized-K and conventional cellular channel models as well. As we investigate performance of the system, first we derive exact cumulative density functions (CDF) of the end-to-end signal-to-noise-ratio. Using this CDF, we obtain the exact closed-form outage probability. Then we derive the exact closed-form symbol error rate (SER) expression for various modulation types. Finally, we verify the analytic results by comparing with computer simulations. Our results show that the outage probability and SER performance decrease when the cascading degrees of the channels increase.

Performance Analysis of Best Relay Selection in Cooperative Wireless Networks

Cooperative communication has been proposed recently in wireless communication systems because of its producing high network reliability and considerable error rate decrease with an extension in the coverage area in wireless networks without need for an increase in the infrastructure. The most challenging problem in implementing cooperation protocols in cooperative wireless networks is the relay selection. This paper proposes a relay selection technique based on Decode-and-Forward (DF) relaying protocol, using the available channel state information (CSI) at the source and the relays. We first establish a closed form symbol error rate (SER) by using the concept of moment generating function (MGF) for both M phase shift keying (MPSK) and M quadrature amplitude modulation (MQAM) signals. By finding the cumulative density function (CDF) and the probability density function (PDF); this facilitated the derivation of a new SER and can propose an optimal power method with relay selection (RS) technique where only the best relay is selected that maximizes the signal-to-noise ratio (SNR) to achieve the transmission process and develop the performance of the system. Finally, simulation results provided good confirmation of the theoretical analysis.

SER performance analysis of MPPM FSO system with three decision thresholds over exponentiated Weibull fading channels

In this work, the symbol error rate (SER) performance of the multiple pulse position modulation (MPPM) based free-space optical communication (FSO) system with three different decision thresholds, fixed decision threshold (FDT), optimized decision threshold (ODT) and dynamic decision threshold (DDT) over exponentiated Weibull (EW) fading channels has been investigated in detail. The effects of aperture averaging on each decision threshold under weak-to-strong turbulence conditions are further studied and compared. The closed-form SER expressions for three thresholds derived with the help of generalized Gauss–Laguerre quadrature rule are verified by the Monte Carlo simulations. This work is helpful for the design of receivers for FSO communication systems.

Closed Form SER Expressions for QPSK OFDM Systems With Frequency Offset in Rayleigh Fading Channels

In this letter, the performance of QPSK OFDM systems with frequency offsets is investigated. Closed form expressions for the symbol error rate (SER) that are valid for any frequency offset in Rayleigh fading channels are derived. To achieve this, a modification to the result of the integral of the product of two Q-functions over the Rayleigh distribution is provided. The modification makes the result of this integral valid in any case whether the arguments of the Q-functions are positive or negative. Simulation results are provided to demonstrate the accuracy of the derived expressions.

Towards Resource Allocation Algorithm in Opportunistic Relaying Cooperative UWB Communication System

A novel communication system named cooperative is proposed by bringing OR (Opportunistic Relaying) to UWB system. Particularly, the exact and closed-form symbol error rate (SER) expression is derived firstly in this paper. In order to maximize the capacity considering fairness between users, a definition of equivalent mean channel gain is given, and a joint resource allocation algorithm is also proposed which includes three steps: sub-band allocation algorithm, relaying allocation algorithm and power allocation algorithm. Employing the conception of relative requirement degree, the algorithm shows a distributed solution targeting relay partner selecting and increasing capacity while satisfying the users' QoS (Quality of Service) requirement. Simulations results validate the performance of the proposed algorithm.

Performance Comparisons of Optimal Power Allocation over Nakagami-m and Rayleigh Fading Channels in Wireless Cooperative Systems

Cooperative wireless communication has been newly proposed in wireless communication systems for discovering the inherent spatial diversity in relay channels. The Amplify- and-Forward (AF) cooperation protocols with multiple relays have not been sufficiently examined; however, it has a low complexity in terms of application. Through this article, we evaluate a cooperative diversity technique whereby a source broadcasts some data to a destination with the assistance of multiple relay nodes with AF protocols, by taking into account the challenge of allocating power to be able to increase the total capacity of AF and also enhance resource utilization. We analyse the optimality of how much the power should really be allocated at the source as well as relays system by optimizing the symbol error rate (SER) performance in a useful method on the basis of Rayleigh and Nakagami- m fading. Firstly, we derive a closed-form SER formulation for MPSK signal making use of the idea of moment generating function (MGF) and some statistical approximations in high signal to noise ratio (SNR) for the system under studied. We therefore determine a tight corresponding lower bound, which converges to the identical limit the same as the theoretical upper bound, after that develops an optimal power allocation (OPA) strategy with mean channel gains over Rayleigh and also Nakagami- m fading to reduce the SER. Simulation results prove that our approach using Nakagami- m fading outperforms the (OPA) using Raleigh fading scheme and is tight with the theoretical approximation based on the SER upper bound in high SNR for a different number of relays .  Index Terms—Wireless communication, amplify-and-forward, symbol error rate, Nakagami- m fading, power allocation.

Generalised closed-form symbol error rate analysis for Orthogonal Space-Time Block Coded OFDM system

In this paper, the Symbol Error Rate (SER) performance for Orthogonal Space- Time Block Coded (OSTBC) Orthogonal Frequency Division Multiplexing (OFDM) systems over Nakagami-m fading channels is analysed. A novel closed-form SER expression is proposed, which incorporates the Gauss hypergeometric function and Appell hypergeometric function into the conventional Probability Density Function (PDF) approach. The proposed exact closed-form SER expression is a generalised solution since it perfectly captures OSTBCOFDM systems' performances when having different antenna configurations that employ various modulation schemes and which experience various fading conditions. Finally, Monte Carlo simulation results are provided to demonstrate the exact match between the simulation results and the proposed analytical expressions.